Level Zero G-Types

Abstract

Let G be a connected reductive group defined over a local non Archimedean field F with residue field F; let P be a parahoric subgroup with associated reductive quotient M. If σ is an irreducible cuspidal representation of M(F) it provides an irreducible representation of P by inflation. We show that the pair (P,σ) is an (σ) and they imply that the appropriate parabolic induction functor and its left adjoint can be realised algebraically via pullbacks from ring homomorphisms.